This tag is for questions seeking external references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.

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3answers
379 views

Chernoff bounds - basic results

I am looking for a good reference covering Chernoff bounds for a beginner. By this I mean, a beginner on the subject of Chernoff bounds; I have taken an undergraduate and masters course in mathematics ...
3
votes
1answer
413 views

Reference request: preparation for learning a little smooth infinitesimal analysis?

I'm interested in learning a little smooth infinitesimal analysis. There is a free book by Kock: Smooth Differential Geometry, http://home.imf.au.dk/kock/ . As I dive into it, I feel that I'm not ...
1
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2answers
1k views

What book are good to learn about limits and continuity for the first time?

I've tried reading about "open balls", limits, and continuity, but I just don't get the stuff about " given epsilon > 0 find delta > 0 such that ... < delta implies that ... < epsilon". I've ...
5
votes
1answer
2k views

Mean distance from origin after $N$ equal steps of Random-Walk in a $d$-dimensional space.

I am looking for a formula that evaluates the mean distance from origin after $N$ equal steps of Random-Walk in a $d$-dimensional space. Such a formula was given by "Henry" to a question by "Diego" ...
10
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3answers
4k views

A digital notebook for Mathematics?

When I studied math 15 years ago, I was dreaming of having a math repository with tags to navigate between the different entries. I imagined it would come eventually to the market, and was hopefull ...
3
votes
1answer
433 views

Thrice-punctured sphere

This claim is made in the book Quantum Triangulations (eds.: Carfora, Marzuoli), p.45: the thrice-punctured sphere is the largest subdomain of $\mathbb{S}^2$ supporting a hyperbolic metric. I ...
1
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1answer
106 views

Algebras over a field and equivalence of module categories

Let $k$ be a field. Let $A$ be a finitely generated $k$-algebra. Consider the inclusion of the center $i:Z(A)\hookrightarrow A$. I'm interested in what general conditions there are for the pull-back ...
1
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1answer
194 views

Is it possible to have a cosine of 1.0000

I was given a triangle: side opposite of angle A: unknown, referred to as L side adjacent of angle A: 11' hypotenuse: 14' I have to find the cosine of angle A, the degrees, and the length of "L", ...
1
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0answers
263 views

Basic Questions on Evaluating $ \int_C g(t) d(f(t)+f(at))$

Suppose the following complex integral over a countour $C$: $$ \int_C g(t) d(f(t)+f(at)), $$ where $f(t)$ is a complex-valued function. My questions are: Is this possible at all? Definition of ...
0
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1answer
85 views

Do these ideals have names?

Given a ring $R$ and an ideal(two-sided) $I\subset R$, we find an ideal $$[R:I]=\{x\in R| xR\subset I \}$$ It is easy to see that this ideal coincides with the original ideal $I$ if $I$ is a prime ...
7
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1answer
385 views

Holomorphic function of a matrix

A statement is made below. The questions are: (a) Is the statement true? (b) If it is, does it appear in the literature? Here is the statement. For any matrix $A$ in $M_n(\mathbb C)$, write ...
1
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1answer
284 views

Pinched torus generalization

The pinched torus is homeomorphic to a sphere with two (different) points identified.           What is the name and topological structure of the ...
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10answers
2k views

Reference for general-topology

Though there are several posts discussing the reference books for topology, for example best book for topology. But as far as I looked up to, all of them are for the purpose of learning topology or ...
5
votes
2answers
677 views

Reference for the subgroup structure of $PSL(2,q)$

This material is covered in detail in Dickson's "Linear Groups with an exposition of the Galois Field Theory", chapter XXII and Huppert's "Endliche Gruppen", chapter II, paragraph 8. Since I don't ...
7
votes
1answer
538 views

Existence of non-atomic probability measure

The Question Let $X$ be a set. Let $\mathcal{F}\subseteq P(X)$ be a $\sigma$-algebra. (Or, if it makes a difference, let $X$ be a topological space and $\mathcal{F}$ the Borel sets.) When can we ...
6
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1answer
452 views

completeness of the theory of real numbers

The theory of natural numbers (such as Peano axioms) is incomplete due to Gödel's incompleteness theorem. But, I heard that the theory of real numbers is complete (edit: not in the sense of ...
4
votes
1answer
302 views

Online tutorial requested: functional derivatives

I am taking a course on Quantum Field Theory where we work alot with the functional derivative. Does anyone know of a good, free online PDF tutorial with some examples? Cheers!
0
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1answer
631 views

References to re-learn differentiation and integration

I'm looking to re-learn "differentiation and integration", it has really been a long time since I touched the subject. I'm considering starting with Algebra then differentiation and integration. ...
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4answers
2k views

What algebraic topology book to read after Hatcher's?

I've currently finished chapter 2 of his book and done all the exercises of in chapter 0, 1 and 2. Was wondering when I finished reading this book what book do I read next in algebraic topology?
2
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0answers
24 views

Spaces of functions on subsets and linear mappings

I have been looking for research concerned with the following construct: Let $X$ be a set (most likely with a topology) and let $R$ be a subset of the family of all subsets of $X$. $R$ could be the ...
2
votes
2answers
848 views

Computation of the probability density function for $(X,Y) = \sqrt{2 R} ( \cos(\theta), \sin(\theta))$

Let $R$ be a almost surely non-negative continuous random variable with absolutely continuous measure, and $\Theta$ be an independent random variable, uniformly distributed on the interval $[0, 2 ...
7
votes
1answer
314 views

Dynkin diagram automorphisms and weights

Let $\sigma$ be a nontrivial Dynkin diagram automorphism of a finite-dimensional complex simple Lie algebra $\frak g$ (of type A, D or E) and let $\frak h$ be a Cartan subalgebra of $\frak g$. Let $I$ ...
4
votes
2answers
168 views

Is there a well-defined notion of class-dimensional vector spaces?

I was thinking a bit about isometric embeddings into Hilbert spaces and got the following idea. First, as we recall, many vector spaces over the reals are isomorphic to $\mathbb{R}^{\alpha}$ for some ...
5
votes
1answer
644 views

Video of Terence Tao on Poincaré's Conjecture

Last year, I found a video of Terence Tao on the Poincaré Conjecture, which could be downloaded in mp4 format. I did downloaded it, however I had to format my computer, then I lost it. I searched in ...
12
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2answers
1k views

classical solutions of PDE with mixed boundary conditions

Nowadays people usually consider PDEs in weak formulations only, so I have a hard time finding statements about the existence of classical solutions of the Poisson equation with mixed ...
2
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2answers
189 views

Shortest paths of undirected graphs with modular weights

Let $G=(V,E,W)$ be an undirected weighted graph, where $V$ (resp. $E$) is the set of vertices (resp. edges) of $G$, and $W : E \to \mathbb{Z}_p$ is the edge weight assignment function. Note that ...
4
votes
3answers
718 views

Books for Numerical linear algebra

I'am looking for some books for studying Numerical linear algebra methods. It could be on english or russian ​​languages, and Maple or Matlab examples preferable, but it also can be C/C++/Formal code. ...
7
votes
2answers
928 views

Chern numbers of Projective Space

Consider the $k$-th chern class $c_k:=c_k(\mathcal{T}_{\mathbb{P}^n})$ of the tangent sheaf of projective space $\mathbb{P}^n=\mathbb{P}^n_\Bbbk$ over some (algebraically closed, if you want) field ...
2
votes
1answer
227 views

How many solutions for $x^2 = 1$?

Let $F$ be an non-archimedean local field, let $o$ be its ring of integers, and let $p$ be the maximal ideal Is there a closed form for the cardinality $$ | \{ x \in o / p^N: x^2 = -1 \bmod p^N\} | ...
3
votes
1answer
149 views

Solving SDE's on subsets of $R^n$.

It is well-known (see for instance Oskendal's text) that if $T>0$ and $$b(\cdot,\cdot): [0,T] \times \mathbb{R}^n \rightarrow \mathbb{R}^n~~~~~~\sigma(\cdot,\cdot):[0,T] \times \mathbb{R}^n ...
2
votes
0answers
84 views

Scale invariance and $1/f^2$ power spectrum

In the paper Occlusion Models for Natural Images : A Statistical Study of a Scale-Invariant Dead Leaves Model; Lee, A. B. Mumford, D. B. Huang, J.; International Journal of Computer Vision I read ...
2
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0answers
126 views

Useful Bounds for Fractional Part-Power Summations

Are there useful lower and upper (preferably sharp or asymptotic) bounds for the following fractional part-power summation? Given arbitrary reals $a, b > 1$ and integer $n \geqslant 1$, let ...
5
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2answers
1k views

Translation Request - Grothendieck's Tohoku Paper

I've been learning sheaf cohomology, and was interested in reading Grothendieck's Tohoku paper. However, I don't read French. I've done a semi-extensive google search, and the majority of links end ...
2
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2answers
308 views

Statistics resources with examples for a C.S. student

I'm a computer science student and is fairly familiar with basic probability (calculating the probability of a event occurring, pmfs and pdfs) but I find it very difficult to grasp the concepts of ...
1
vote
1answer
76 views

References for the “reduced power” of a group

Let $G$ be a countable group. Consider the subgroup $$\widetilde{\Pi}G = \left\{(g_n) \in \prod\nolimits_{\mathbb{N}} G\,:\,g_n \neq e\text{ only for finitely many }n\right\}$$ of the countable power ...
2
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0answers
114 views

explicit error bounds for Multivariate interpolation

I want to interpolate a function of $d$ variables over a Cartesian grid, using multivariate interpolation, while characterizing interpolation error in terms of bounds on partial derivatives of the ...
20
votes
3answers
709 views

Reference request for Geometric Group Theory

I am doing a reading course this semester on Geometric Group Theory. I have been following A Course on Geometric Group Theory by Bowditch. The professor who is guiding me is not aware of good ...
6
votes
5answers
994 views

Good book on integral equation?

I'm looking for a good reference on integral equations (i.e., an equation in which an unknown function appears under an integral sign such as the Fredholm equation). I would like something accessible ...
4
votes
2answers
432 views

Best book to learn local cohomology with a global point of view

Can anyone suggest me some book that we can use for studying local cohomology, with a global view to many different area of maths, i.e to Commutative Algebra, Number Theory, Algebraic Geometry.... I ...
2
votes
3answers
137 views

Concise ODEs reference?

Is there any text that I can use as a short reference for the standard techniques for solving basic ODEs? I currently have been using Boyce and diPrima as my ODEs text, and it is far too wordy for my ...
7
votes
3answers
843 views

Looking for a Calculus Textbook

I want to start signal processing and I need a book that satisfies my mathematical requirements: I am in the third grade of high school and I don't know any useful thing about limit, differential, ... ...
2
votes
1answer
227 views

Reference request for Optimal Stopping (Stochastic Analysis)

I would like to start and get into the habit of reading some publications in different areas of mathematics, to get used to the writing style / mathematical sophistication etc. that is expected. In ...
4
votes
0answers
209 views

Proving NP-completeness (hardness) exercises

I am looking for a list of exercises that can be done to practice polynomial time reductions to prove NP-hardness of problems. I know there are hundreds (thousands?) of problems proven to be NP-hard. ...
5
votes
1answer
295 views

Arithmetic progressions

What are the largest known lower bounds for $B_k$, the maximal sum of the reciprocals of the members of subsets of the positive integers which contain no arithmetic progressions of length $k$? for ...
2
votes
2answers
98 views

Simplicial Homotopy Theory (References)

I'd like to know some good references,introductory or not in Simplicial Homotopy Theory. Thanks.
16
votes
4answers
5k views

Good introductory book on fluid dynamics

I am interested in getting a good introductory book to fluid dynamics. I am a first year PhD student in Mathematics. My project involves a simplification of the Navier-Stokes equations. But I don't ...
10
votes
2answers
829 views

Proof $\mathbb{A}^n$ is irreducible, without Nullstellensatz

As the title suggests, could anyone either provide me with or direct me to a proof that affine n-space $\mathbb{A}^n$ is irreducible, without using the Nullstellensatz? This is an exercise in a ...
10
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3answers
410 views

Should I look at syllabi for math courses before beginning my bachelor's degree in math?

Next year I'll start my bachelor's degree on mathematics, but I want to study something about it while I'm idle. I've found this: http://webdocs.registrar.fas.harvard.edu/courses/Mathematics.html ...
5
votes
3answers
424 views

Rigorous book on bootstrapping, boosting, bagging, etc.

Is there a mathematically rigorous book giving an introduction to boosting, etc. A book that is rigorous like "A Course in Probability Theory" by Kai Lai Chung.
2
votes
3answers
269 views

Differential forms and double improper integral

Can someone suggest me a list of book or workbook with examples and solutions on differential forms and double improper integral?